A Special Family of m-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition

Aldawish, Ibtisam; Swamy, S. R.; Frasin, B. A.

doi:10.3390/fractalfract6050271

Cited by 10 publications

(11 citation statements)

References 31 publications

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“…Remark 5. The family B τ σ κ (η, ) ≡ W τ σ κ (η, 0, ), 0 < ≤ 1, τ ≥ 1, was investigated by Aldawish et al [24].…”

Section: The Function Familymentioning

confidence: 99%

“…The momentum on investigations of functions in certain subfamilies of σ κ was gained in recent years due to the paper [16] and it has led to a large number of papers on subfamilies of σ κ [17][18][19][20]. Inspired by these works, many researchers have investigated several interesting subfamilies of σ κ and found non-sharp estimates on initial coefficients and the Fekete-Szegö functional problem |d 2κ+1 − δd 2 κ+1 |, δ ∈ [21] of functions belonging to these subfamilies (see, for example [22][23][24][25]) and this continued to appear in [26,27], showing the developments in the subject area of this paper.…”

Section: Introductionmentioning

confidence: 99%

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On τ-Pseudo-ν-Convex κ-Fold Symmetric Bi-Univalent Function Family

Swamy¹,

Cotîrlǎ

2022

Symmetry

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The object of this article is to explore a τ-pseudo-ν-convex κ-fold symmetric bi-univalent function family satisfying subordinations condition generalizing certain previously examined families. We originate the initial Taylor–Maclaurin coefficient estimates of functions in the defined family. The classical Fekete–Szegö inequalities for functions in the defined τ-pseudo-ν-convex family is also estimated. Furthermore, we present some of the special cases of the main results. Relevant connections with those in several earlier works are also pointed out. Our study in this paper is also motivated by the symmetry nature of κ-fold symmetric bi-univalent functions in the defined class.

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“…Remark 5. The family B τ σ κ (η, ) ≡ W τ σ κ (η, 0, ), 0 < ≤ 1, τ ≥ 1, was investigated by Aldawish et al [24].…”

Section: The Function Familymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On τ-Pseudo-ν-Convex κ-Fold Symmetric Bi-Univalent Function Family

Swamy¹,

Cotîrlǎ

2022

Symmetry

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“…Some fascinating uses of differential and integral operators are highlighted in a recent survey-cum-expository review study [8]. Some examples of publications on the extension of Sȃlȃgean differential operators are included in [9,10], with examples of q-extensions in [11][12][13][14][15][16][17][18]).…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Some New Applications of the q-Analogous of Differential and Integral Operators for New Subclasses of q-Starlike and q-Convex Functions

et al. 2023

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In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications in numerical analysis and the solution of differential equations. Many topics, including complex analysis, hypergeometric series, and particle physics, have been generalized in q-calculus. In this study, first of all, we define the q-analogues of a differential operator (DRλ,qm,n) by using the basic idea of q-calculus and the definition of convolution. Additionally, using the newly constructed operator (DRλ,qm,n), we establish the q-analogues of two new integral operators (Fλ,γ1,γ2,…γlm,n,q and Gλ,γ1,γ2,…γlm,n,q), and by employing these operators, new subclasses of the q-starlike and q-convex functions are defined. Sufficient conditions for the functions (f) that belong to the newly defined classes are investigated. Additionally, certain subordination findings for the differential operator (DRλ,qm,n) and novel geometric characteristics of the q-analogues of the integral operators in these classes are also obtained. Our results are generalizations of results that were previously proven in the literature.

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“…For a brief history and interesting examples in the family Σ see the pioneering work on this subject by Srivastava et al [24], which actually revived the study of bi-univalent functions in recent years. In a considerably large number of sequels to the aforementioned work of Srivastava et al [24], several different sub families of the bi-univalent function family Σ were introduced and studied analogously by the many authors (see, for example, [2,3,5,11,15,18,22,27,28,30,33]).…”

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confidence: 99%

Two Families of m-fold Symmetric Bi-univalent Functions Involving a Linear Combination of Bazilevic Starlike and Convex Functions

Khachi,

Wanas

2024

EJMS

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In the present paper, we define two new families $K M_{\Sigma_m}(\lambda, \gamma, \delta ; \alpha)$ and $K M_{\Sigma_m}^*(\lambda, \gamma, \delta ; \beta)$ of holomorphic and m-fold symmetric bi-univalent functions associated with the Bazilevic starlike and convex functions in the open unit disk U. We find upper bounds for the first two Taylor-Maclaurin $\left|a_{m+1}\right|$ and $\left|a_{2 m+1}\right|$ for functions in these families. Further, we point out several special cases for our results.

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A Special Family of m-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition

Cited by 10 publications

References 31 publications

On τ-Pseudo-ν-Convex κ-Fold Symmetric Bi-Univalent Function Family

On τ-Pseudo-ν-Convex κ-Fold Symmetric Bi-Univalent Function Family

Some New Applications of the q-Analogous of Differential and Integral Operators for New Subclasses of q-Starlike and q-Convex Functions

Two Families of m-fold Symmetric Bi-univalent Functions Involving a Linear Combination of Bazilevic Starlike and Convex Functions

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